The script originally was intended to be a story featuring the Riddler. However, Frank Gorshin was in the middle of a contract dispute and as a result the script was rewritten for a new villain, the Puzzler, as played by Maurice Evans.
Atremus Knab was largely based on real life millionaire tycoon Howard Hughes, who was widely known for owning interests in the industries of aviation and movie making, among others.
There was an obscure DC (then National) Comics villain called the Puzzler, but he fought Superman, not Batman, and lacked this Puzzler's interest in flight and Shakespeare. It is reasonable to assume that the producers were unaware of this character's existence, since he last appeared in 1943.
The Puzzler's front business is called The Globe Balloon Factory. In keeping with the Puzzler's Shakespearian quotations, this was likely a reference to The Globe Theatre, with which William Shakespeare has been highly associated. The name was also likely a reference to the spherical or globe shape of traditional balloons.